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Finley Taylor

Shaft frequency analyser

Can I predict how fast a golf iron's shaft vibrates when plucked, measure it with a rig built around my phone, and explain any difference?

Planned rig layout, side viewA golf club clamped by its grip in hardwood V-jaws in a bench vice, with the grip butt flush with the outer jaw face. The shaft runs out to the ferrule over the free length L, and the head sits toe up with a 1 gram magnet on its back. A phone sits 6 to 10 centimetres below the head to read the magnet with its magnetometer.Pluck127 mmFree length L6–10 cmGrip butt flushHardwood V-jawsBench viceHead, toe up1 g magnetPhone, phyphox
Planned rig layout from my build plan, side view, not to scale. The circled dot marks the pluck direction: the head is pulled 50–75 mm towards you, out of the page, and released.

The question

Club fitters judge how stiff a shaft is by how fast it vibrates: clamp the grip, pluck the head and count the swings per minute (CPM, cycles per minute). Through a set of irons, the number changes by about 4 CPM for every half inch of length. I want to predict that number for a real iron, measure it on a rig I build, and explain any difference.

I set these targets before testing:

What I'm aiming forTarget
The same reading when I pluck again without moving the clubWithin ±0.5 CPM
The same reading after unclamping and clamping againWithin ±1.5 CPM
Steel test bar, 0.9 m out of the clamp, against its textbook answerWithin 2%
Fusion simulation of the bar against the textbook answerWithin 0.5%
Club model against measurementFind the biggest source of error, and how big it is

The two repeatability targets are one standard deviation.

Prediction

I'll predict the frequency three ways, and record each prediction, dated, before I measure a club:

  1. a hand calculation giving upper and lower limits, from how stiff the shaft is at the grip end and at the tip;
  2. a model in MATLAB that works the frequency out from the shape the tapered shaft bends into (a Rayleigh model);
  3. a vibration simulation in Fusion, refined until the answer stops changing, and checked first on a steel bar with a textbook answer.
Awaiting model, due 4 Oct 2026

Test

The rig is a bench vice with V-shaped hardwood jaws, a 1 g magnet on the back of the club head, and my phone's magnetic sensor recording through the phyphox app. Before testing any club, I check the whole setup on a 10 mm steel bar at three lengths, where the textbook gives an exact answer.

I fit a fading wave (a damped sine) to each pluck, rather than just reading the peak of a frequency plot (an FFT). On an 8-second recording, an FFT can only tell frequencies apart in 7.5 CPM steps: coarser than the 4 CPM difference between neighbouring irons.

Result

Measured against predicted: awaiting test, due 11 Oct 2026

The chart appears here with the club measurements. The prediction is plotted first, then the measured points with their error bars.

The gap explained

Taping coins to the head separates the two things that can make a prediction wrong: the shaft being stiffer or softer than modelled, or the head behaving heavier or lighter. Plotting 1 ÷ (frequency squared) against the coins' mass gives a straight line. Its slope gives the shaft's stiffness at the head, and where it starts, with no coins, gives the head's effective mass.

Awaiting test, due 15 Oct 2026

What I'd do next

Written with Rev C, due 15 Oct 2026

Revision history

RevDateWhat changed
ADue 4 Oct 2026Hand calculation, MATLAB model and Fusion vibration simulation; the steel test bar checked against its textbook answer.
BDue 11 Oct 2026Club measurements and the coin test.
CDue 15 Oct 2026How accurate each measurement is, predicted against measured, and the gap explained.